%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : LCL691^1 : TPTP v9.3.1. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % Computer : n002.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Sep 7 01:02:26 PM UTC 2026 % Result : Theorem 4.96s 5.23s % Output : Proof 4.96s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL691^1 : TPTP v9.3.1. Released v3.7.0. % 0.00/0.04 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.09/0.36 % Computer : n002.cluster.edu % 0.09/0.36 % Model : x86_64 x86_64 % 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.36 % Memory : 8046.5625MB % 0.09/0.36 % OS : Linux 6.8.0-71-generic % 0.09/0.36 % CPULimit : 300 % 0.09/0.36 % WCLimit : 300 % 0.09/0.36 % DateTime : Fri Sep 4 15:33:20 UTC 2026 % 0.09/0.36 % CPUTime : % 4.96/5.23 % SZS status Theorem % 4.96/5.23 % Mode: mode495 % 4.96/5.23 % Inferences: 13 % 4.96/5.23 % SZS output start Proof % 4.96/5.23 thf(ty_relr, type, relr : ($i>$i>$o)). % 4.96/5.23 thf(ty_eigen__2, type, eigen__2 : $i). % 4.96/5.23 thf(ty_eigen__1, type, eigen__1 : $i). % 4.96/5.23 thf(ty_eigen__0, type, eigen__0 : ($i>$o)). % 4.96/5.23 thf(ty_reli, type, reli : ($i>$i>$o)). % 4.96/5.23 thf(ty_eigen__3, type, eigen__3 : $i). % 4.96/5.23 thf(sP1,plain,sP1 <=> (![X1:$i>$o]:(![X2:$i]:((![X3:$i]:(((relr @ X2) @ X3) => (X1 @ X3))) => (X1 @ X2)))),introduced(definition,[new_symbols(definition,[sP1])])). % 4.96/5.23 thf(sP2,plain,sP2 <=> (![X1:$i]:(((relr @ eigen__2) @ X1) => (![X2:$i]:(((reli @ X1) @ X2) => (eigen__0 @ X2))))),introduced(definition,[new_symbols(definition,[sP2])])). % 4.96/5.23 thf(sP3,plain,sP3 <=> ((reli @ eigen__2) @ eigen__3),introduced(definition,[new_symbols(definition,[sP3])])). % 4.96/5.23 thf(sP4,plain,sP4 <=> (eigen__0 @ eigen__3),introduced(definition,[new_symbols(definition,[sP4])])). % 4.96/5.23 thf(sP5,plain,sP5 <=> (sP2 => (![X1:$i]:(((reli @ eigen__2) @ X1) => (eigen__0 @ X1)))),introduced(definition,[new_symbols(definition,[sP5])])). % 4.96/5.23 thf(sP6,plain,sP6 <=> ((![X1:$i]:(((reli @ eigen__2) @ X1) => (![X2:$i]:(((relr @ X1) @ X2) => (![X3:$i]:(((reli @ X2) @ X3) => (eigen__0 @ X3))))))) => sP2),introduced(definition,[new_symbols(definition,[sP6])])). % 4.96/5.23 thf(sP7,plain,sP7 <=> (![X1:$i]:(((reli @ eigen__2) @ X1) => (eigen__0 @ X1))),introduced(definition,[new_symbols(definition,[sP7])])). % 4.96/5.23 thf(sP8,plain,sP8 <=> (![X1:$i>$o]:(![X2:$i]:((![X3:$i]:(((reli @ X2) @ X3) => (X1 @ X3))) => (X1 @ X2)))),introduced(definition,[new_symbols(definition,[sP8])])). % 4.96/5.23 thf(sP9,plain,sP9 <=> (![X1:$i]:(((reli @ eigen__2) @ X1) => (![X2:$i]:(((relr @ X1) @ X2) => (![X3:$i]:(((reli @ X2) @ X3) => (eigen__0 @ X3))))))),introduced(definition,[new_symbols(definition,[sP9])])). % 4.96/5.23 thf(sP10,plain,sP10 <=> (sP3 => sP4),introduced(definition,[new_symbols(definition,[sP10])])). % 4.96/5.23 thf(sP11,plain,sP11 <=> (![X1:$i]:((![X2:$i]:(((relr @ X1) @ X2) => (![X3:$i]:(((reli @ X2) @ X3) => (eigen__0 @ X3))))) => (![X2:$i]:(((reli @ X1) @ X2) => (eigen__0 @ X2))))),introduced(definition,[new_symbols(definition,[sP11])])). % 4.96/5.23 thf(sP12,plain,sP12 <=> (![X1:$i]:((![X2:$i]:(((reli @ X1) @ X2) => (![X3:$i]:(((relr @ X2) @ X3) => (![X4:$i]:(((reli @ X3) @ X4) => (eigen__0 @ X4))))))) => (![X2:$i]:(((relr @ X1) @ X2) => (![X3:$i]:(((reli @ X2) @ X3) => (eigen__0 @ X3))))))),introduced(definition,[new_symbols(definition,[sP12])])). % 4.96/5.23 thf(def_mfalse,definition,(mfalse = (^[X1:$i]:$false))). % 4.96/5.23 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))). % 4.96/5.23 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))). % 4.96/5.23 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))). % 4.96/5.23 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(~(((X1 @ X3) => (~((X2 @ X3))))))))))). % 4.96/5.23 thf(def_mimpl,definition,(mimpl = (^[X1:$i>$o]:(mor @ (mnot @ X1))))). % 4.96/5.23 thf(def_miff,definition,(miff = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimpl @ X1) @ X2)) @ ((mimpl @ X2) @ X1)))))). % 4.96/5.23 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))). % 4.96/5.23 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(~((![X4:$i]:(((X1 @ X3) @ X4) => (~((X2 @ X4)))))))))))). % 4.96/5.23 thf(def_mall,definition,(mall = (^[X1:individuals>$i>$o]:(^[X2:$i]:(![X3:individuals]:((X1 @ X3) @ X2)))))). % 4.96/5.23 thf(def_mexists,definition,(mexists = (^[X1:individuals>$i>$o]:(^[X2:$i]:(~((![X3:individuals]:(~(((X1 @ X3) @ X2)))))))))). % 4.96/5.23 thf(def_mvalid,definition,(mvalid = (!!))). % 4.96/5.23 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))). % 4.96/5.23 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))). % 4.96/5.23 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))). % 4.96/5.23 thf(def_cs4_atom,definition,(cs4_atom = (mbox @ reli))). % 4.96/5.23 thf(def_cs4_and,definition,(cs4_and = mand)). % 4.96/5.23 thf(def_cs4_or,definition,(cs4_or = mor)). % 4.96/5.23 thf(def_cs4_impl,definition,(cs4_impl = (^[X1:$i>$o]:(^[X2:$i>$o]:((mbox @ reli) @ ((mimpl @ X1) @ X2)))))). % 4.96/5.23 thf(def_cs4_true,definition,(cs4_true = mtrue)). % 4.96/5.23 thf(def_cs4_false,definition,(cs4_false = mfalse)). % 4.96/5.23 thf(def_cs4_all,definition,(cs4_all = (^[X1:individuals>$i>$o]:((mbox @ reli) @ (mall @ X1))))). % 4.96/5.23 thf(def_cs4_box,definition,(cs4_box = (^[X1:$i>$o]:((mbox @ reli) @ ((mbox @ relr) @ X1))))). % 4.96/5.23 thf(def_cs4_valid,definition,(cs4_valid = mvalid)). % 4.96/5.23 thf(cs4_refl,conjecture,(![X1:$i>$o]:(![X2:$i]:(![X3:$i]:(((reli @ X2) @ X3) => ((~((~((![X4:$i]:(((reli @ X3) @ X4) => (![X5:$i]:(((relr @ X4) @ X5) => (![X6:$i]:(((reli @ X5) @ X6) => (X1 @ X6))))))))))) => (![X4:$i]:(((reli @ X3) @ X4) => (X1 @ X4))))))))). % 4.96/5.23 thf(h0,negated_conjecture,(~((![X1:$i>$o]:(![X2:$i]:(![X3:$i]:(((reli @ X2) @ X3) => ((![X4:$i]:(((reli @ X3) @ X4) => (![X5:$i]:(((relr @ X4) @ X5) => (![X6:$i]:(((reli @ X5) @ X6) => (X1 @ X6))))))) => (![X4:$i]:(((reli @ X3) @ X4) => (X1 @ X4)))))))))),inference(assume_negation,[status(cth)],[cs4_refl])). % 4.96/5.23 thf(h1,assumption,(~((![X1:$i]:(![X2:$i]:(((reli @ X1) @ X2) => ((![X3:$i]:(((reli @ X2) @ X3) => (![X4:$i]:(((relr @ X3) @ X4) => (![X5:$i]:(((reli @ X4) @ X5) => (eigen__0 @ X5))))))) => (![X3:$i]:(((reli @ X2) @ X3) => (eigen__0 @ X3))))))))),introduced(assumption,[])). % 4.96/5.23 thf(h2,assumption,(~((![X1:$i]:(((reli @ eigen__1) @ X1) => ((![X2:$i]:(((reli @ X1) @ X2) => (![X3:$i]:(((relr @ X2) @ X3) => (![X4:$i]:(((reli @ X3) @ X4) => (eigen__0 @ X4))))))) => (![X2:$i]:(((reli @ X1) @ X2) => (eigen__0 @ X2)))))))),introduced(assumption,[])). % 4.96/5.23 thf(h3,assumption,(~((((reli @ eigen__1) @ eigen__2) => (sP9 => sP7)))),introduced(assumption,[])). % 4.96/5.23 thf(h4,assumption,((reli @ eigen__1) @ eigen__2),introduced(assumption,[])). % 4.96/5.23 thf(h5,assumption,(~((sP9 => sP7))),introduced(assumption,[])). % 4.96/5.23 thf(h6,assumption,sP9,introduced(assumption,[])). % 4.96/5.23 thf(h7,assumption,(~(sP7)),introduced(assumption,[])). % 4.96/5.23 thf(h8,assumption,(~(sP10)),introduced(assumption,[])). % 4.96/5.23 thf(h9,assumption,sP3,introduced(assumption,[])). % 4.96/5.23 thf(h10,assumption,(~(sP4)),introduced(assumption,[])). % 4.96/5.23 thf(1,plain,(~(sP1) | sP11),inference(all_rule,[status(thm)],[])). % 4.96/5.23 thf(2,plain,(~(sP11) | sP5),inference(all_rule,[status(thm)],[])). % 4.96/5.23 thf(3,plain,((~(sP5) | ~(sP2)) | sP7),inference(prop_rule,[status(thm)],[])). % 4.96/5.23 thf(4,plain,(~(sP8) | sP12),inference(all_rule,[status(thm)],[])). % 4.96/5.23 thf(5,plain,(~(sP12) | sP6),inference(all_rule,[status(thm)],[])). % 4.96/5.23 thf(6,plain,((~(sP6) | ~(sP9)) | sP2),inference(prop_rule,[status(thm)],[])). % 4.96/5.23 thf(7,plain,(~(sP7) | sP10),inference(all_rule,[status(thm)],[])). % 4.96/5.23 thf(8,plain,((~(sP10) | ~(sP3)) | sP4),inference(prop_rule,[status(thm)],[])). % 4.96/5.23 thf(refl_axiom_r,axiom,(![X1:$i>$o]:(mvalid @ ((mimpl @ ((mbox @ relr) @ X1)) @ X1)))). % 4.96/5.23 thf(9,plain,sP1,inference(preprocess,[status(thm)],[refl_axiom_r]). % 4.96/5.23 thf(refl_axiom_i,axiom,(![X1:$i>$o]:(mvalid @ ((mimpl @ ((mbox @ reli) @ X1)) @ X1)))). % 4.96/5.23 thf(10,plain,sP8,inference(preprocess,[status(thm)],[refl_axiom_i]). % 4.96/5.23 thf(11,plain,$false,inference(prop_unsat,[status(thm),assumptions([h9,h10,h8,h6,h7,h4,h5,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,h6,h9,h10,9,10])). % 4.96/5.23 thf(12,plain,$false,inference(tab_negimp,[status(thm),assumptions([h8,h6,h7,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h9,h10])],[h8,11,h9,h10])). % 4.96/5.23 thf(13,plain,$false,inference(tab_negall,[status(thm),assumptions([h6,h7,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__3)],[h7,12,h8])). % 4.96/5.23 thf(14,plain,$false,inference(tab_negimp,[status(thm),assumptions([h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,13,h6,h7])). % 4.96/5.23 thf(15,plain,$false,inference(tab_negimp,[status(thm),assumptions([h3,h2,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,14,h4,h5])). % 4.96/5.23 thf(16,plain,$false,inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__2)],[h2,15,h3])). % 4.96/5.23 thf(17,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,16,h2])). % 4.96/5.23 thf(18,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,17,h1])). % 4.96/5.23 thf(0,theorem,(![X1:$i>$o]:(![X2:$i]:(![X3:$i]:(((reli @ X2) @ X3) => ((~((~((![X4:$i]:(((reli @ X3) @ X4) => (![X5:$i]:(((relr @ X4) @ X5) => (![X6:$i]:(((reli @ X5) @ X6) => (X1 @ X6))))))))))) => (![X4:$i]:(((reli @ X3) @ X4) => (X1 @ X4)))))))),inference(contra,[status(thm),contra(discharge,[h0])],[18,h0])). % 4.96/5.23 % SZS output end Proof 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